Integral equations for flexural scattering problems with periodic boundaries

TL;DR

This paper introduces an efficient integral equation method using Floquet-Bloch transform for simulating flexural wave scattering on periodic structures in thin plates, applicable to complex junctions.

Contribution

The paper presents a novel integral equation approach based on quasi-periodic Green's functions for flexural wave scattering, enabling accurate simulations of periodic boundary problems.

Findings

Efficient computation of flexural wave scattering on periodic structures.

Accurate simulation of junctions of semi-infinite lines of scatterers.

Use of Floquet-Bloch transform to decouple problems.

Abstract

We develop a method for computing the scattering of flexural waves off of a periodic wall or a periodic line of scatterers. These waves model the fluctuations of thin plates with periodic clamped, supported, or free edges. We use the Floquet-Bloch transform to convert the problem into a collection of uncoupled quasi-periodic problems. We then solve each quasi-periodic problem efficiently and accurately using a novel integral equation based on the quasi-periodic flexural Green's function. Finally, we show how the proposed method can be used to simulate scattering from junctions of semi-infinite lines of scatterers.